Inter-distance Constraint: An Extension of the All-Different Constraint for Scheduling Equal Length Jobs

Abstract

Abstract. We study a global constraint, the "inter-distance constraint" that ensures that the distance between any pair of variables is at least equal to a given value. When this value is 1, the inter-distance constraint reduces to the all-different constraint. We introduce an algorithm to propagate this constraint and we show that, when domains of the variables are intervals, our algorithm achieves arc-B-consistency. It provides tighter bounds than generic scheduling constraint propagation algorithms (like edge-finding) that could be used to capture this constraint. The worst case complexity of the algorithm is cubic but it behaves well in practice and it drastically reduces the search space. Experiments on special Job-Shop problems and on an industrial problem are reported.

The K King Problem, an Abstract Model for Computing Aircraft Landing Trajectories: On Modeling a Dynamic Hybrid System with Constraints

“…However, initial experiments have shown that this almost never happens while the use of additional variables is costly. Recently, Artiouchine and Baptiste (2005) and Quimper et al (2006) studied the "interdistance constraint" that ensures that the distance between any pair of variables is at least equal to a given value. They describe a polynomial time algorithms to achieve arc-B-consistency (arc-consistency restricted to bounds of domains).…”